Mukuro was an interesting character on the show. During the current timeline, she was the strongest demon by a little bit.
She recruited Hiei because he was bored and needed something to do, LOL.
He impresses her quite a bit, and she reveals that she was a woman.
Her backstory was quite tragic. She was a former slave who fought her way out of servitude.
But the core of her power rested in her hatred for her time being a slave.
She jumped on the idea of a Demon World Tournament.
She ironically goes up against Hiei, whom she defeats. But he managed to give her peace, ironically taking away a lot of her strength.
And she loses the tournament near the end. And she does very little after that.